On the Calculation of the Potential Flow Around Airfoils in Cascade

Abstract

TN ORDER TO IMPROVE the aerodynamic properties of airfoils in cascade, it is necessary to have a convenient method for the calculation of the potential velocity field. The method of conformal transformation, in our opinion, is much too complicated for practical purposes; only the where the airfoil is replaced by a certain distribution of vortices and sources and sinks, seems adequate. In some recent papers,1-3 the singularity method has been applied to airfoils in cascade. The calculations on these lines can still be simplified considerably, as we have shown in a paper7 to be published shortly in detail and an extract of which may be given here. Our method has already been applied with good success to the calculation of boundary layers on airfoils in cascade.8 According to the singularity method, each airfoil of the cascade is replaced by a continuous distribution of vortices and sources (and sinks), situated on the mean line of each profile. The main problem is to calculate the field of induced velocities due to these singularities. In the complex z = x + iy-plane (Fig. 1), an infinite row of elements of singularity of strength g-dz' may be given situated on a straight line through the origin inclined at the angle X against the ;y-axis. The distance of the airfoils being /, these elements have the complex coordinate